Abstract
Upper and lower bounds on the asymptotic behavior of Im F(s, t)=A(s, v) and its higher derivatives on v for large s with v fixed to small non-positive values are derived using the results from axiomatic quantum field theory. Here, F(s, t) is a certain elastic scattering amplitude, sand t are the usual Mandelstam variables, v=t(ln(s/s 0))2 and s0 is an unknown scaling factor. The rough forms of the results are : i) C1 < A(s, v) < C2 for v1<v<O, S~co 84oo
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